Deep neural network classifiers are vulnerable to small input perturbations carefully generated by the adversaries. Injecting adversarial inputs during training, known as adversarial training, can improve robustness against one-step attacks, but not for unknown iterative attacks. To address this challenge, we propose to utilize embedding space for both classification and low-level (pixel-level)...

This paper deals with the iterative solution of large sparse symmetric positive definite systems. We investigate preconditioning techniques of the two-level type that are based on a block factorization of the system matrix. Whereas the basic scheme assumes an exact inversion of the submatrix related to the first block of unknowns, we analyze the effect of using an approximate inverse instead. W...